Ancient solutions in Lagrangian mean curvature flow

Ancient solutions of Lagrangian mean curvature flow in Cn naturally arise as Type II blow-ups. In this extended note we give structural and classification results for such ancient solutions in terms of their blow-down and, motivated by the Thomas–Yau Conjecture, focus on the almost calibrated case. In particular, we classify Type II blow-ups of almost calibrated Lagrangian mean curvature flow when the blow-down is a pair of transverse planes or, when n = 2, a multiplicity two plane. We also show that the Harvey–Lawson Clifford torus cone in C3 cannot arise as the blow-down of an almost calibrated Type II blow-up.